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Interactive visual data analysis is most productive when users can focus on answering the questions they have about their data, rather than focusing on how to operate the interface to the analysis tool. One viable approach to engaging users in interactive conversations with their data is a natural language interface to visualizations. These interfaces have the potential to be both more expressive and more accessible than many other interaction paradigms. In this paper, we focus on supporting a natural flow in data conversations by considering pragmatics, or the ways in which context in a conversation influences meaning. We explore the requirements of a pragmatics component in a natural language system for visualizations and the research challenges that arise in understanding the context of data-related conversations. We then summarize how many of these challenges are generalizable to other settings and contexts involving natural language interfaces.